Is it possible to have Spotify output audio from one sound card and a game output from another sound card at the same time?
No. The OS will only allow you to select one sound card. And for the software you are referring to, as it is today, it is not likely.
However, sound cards can have multiple outputs. Meaning, depending on the settings of your software, you could select software1 to use SoundCard channels 1 and 2, and software2 to use SoundCard channels 3 and 4.
This type of hardware is typically used by musicians and recording engineers. This is what I use and as you can see there are many ins and outs (where outs are the only thing you'd be interested in):
The interface can be PCI, PCI-E, Firewire or USB and can be as cheap as about ~£100/~125euro/~$150 to as much as you want to spend.
This means you can take your outputs to 2 separate speaker pairs.
So, before you go out and buy something, see if you have any option in your software for selecting what sound card to use because if you don't have that option, then you have no options other than the default selected by Windows!